CAPE GIRARDEAU, Missouri (CNN) -- Timothy Krajcir got away with murder for decades, police say. They say he preyed on women he could easily overpower. He always struck at night to avoid detection. When he killed, he never spoke of it to anyone. Police even say they considered a cop might be behind the killings.

Timothy Krajcir in August after authorities say he confessed to killing Deborah Sheppard in 1982.

Authorities now say he may have honed his serial killing skills in the classroom, learning how police investigated crimes and figuring out ways to outsmart them.

Ironically, it was under a court-mandated order from a rape conviction that Krajcir got his degree at Southern Illinois University, Carbondale, where he graduated in December 1981 with a major in administrative justice, typically taken by those looking to enter law enforcement.

His undoing ultimately was something he could never have anticipated at the time -- DNA technology that would connect him to a murder and rape more than 25 years later.

Krajcir, who spent time for rape and other offenses over the years, apparently knew his killing spree eventually would catch up with him.

"I've had conversations with him where he's acknowledged that as the science grew, he knew that at some point this day was going to arrive," Carbondale, Illinois, police Lt. Paul Echols told CNN.

He pleaded guilty in August to the 1982 murder of Southern Illinois University classmate Deborah Sheppard, which helped investigators in Cape Girardeau, Missouri, charge him in five murder cases that had puzzled cops there for years.

In fact, the killings in Cape Girardeau were so calculated police sometimes wondered if they were hunting for one of their own. Victims often were found in their beds, bound, raped and shot in the head -- with few clues to connect any of the slayings together.

"There was some speculation, of course," Cape Girardeau Police Chief Carl Kinnison said when asked if he thought a police officer might have been behind the killings.

Kinnison didn't know it, but as a graduate student he and Krajcir may have crossed paths frequently in the early 1980s on the Southern Illinois campus. Krajcir had been released from prison in 1977 after serving time for rape when he enrolled at the university as a condition of his parole.

He minored in psychology and majored in administrative justice. Kinnison explained why most people choose that major: "Most of the time, it's people that are interested in pursuing a law enforcement career, someone who is interested in getting into police work."

Around the time he enrolled, Krajcir killed five women in Cape Girardeau, an hour's drive from the school's campus, police said. The killings spanned from August 1977 to June 1982. Stalking strangers in other towns was one way he stumped detectives.

"It's very difficult to track someone who comes into your community, commits a crime and then leaves," Kinnison said.

He said Krajcir would stalk victims, break into their homes and wait for them to arrive. He had no connection to the victims or even the town where police said he committed the killings. He was looking for easy, unsuspecting targets, according to police.

Echols of the Carbondale police also was a Southern Illinois student at the same time as Krajcir. He said Krajcir would have learned important investigative information about fingerprints, footwear impressions, hair fiber and other details.

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"He would understand the importance of what we know today as forensic sciences," Echols said.

Police said the killer left behind important evidence at all the crime scenes, but it was never enough to point the finger at anyone.

The break that authorities finally needed came in late August when DNA evidence from the murder and rape of Sheppard, the Southern Illinois student, matched Krajcir, who was serving time at Big Muddy Correctional Center in Ina, Illinois, for parole violations stemming from an array of rape charges. The state had dubbed him a sexually dangerous person.

Authorities then began connecting the dots to the mystery killings in Cape Girardeau, and DNA evidence from one of the crime scenes confirmed it. Semen and a palm print left at the slaying of Mildred Wallace, a 65-year-old who was shot inside her home on June 21, 1982, matched Krajcir, authorities said.

Krajcir then confessed, bringing an end to the killings that had stumped investigators for three decades, police said.

"This is a historic day in the history of crime and punishment in Cape Girardeau," Kennison said last week after charges were finally brought against Krajcir.E-mail to a friend